MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 449 



have varied aiul iittaitied t« a new 8triictiire duriug the course of the evolution of tiie Brachjoiira 

 from Macrourau ancestors. 



Many crabs like the saatl crab, Ocypoda arenaria, spend a good portion of time out of 

 the water and their eyes are admirably adapted for vision in the air, as in tiic case of this species, 

 wiiicli will detect any moving object, such as a man or a dog, a long tlistance oil'. We might thus 

 hope to find a way of escape from the ditticulty in the diversity of habits in the two forms, the 

 lobster being exclusively an aquatic animal. But the ])rimitive Crustacea must have all been 

 aquatic, and the hermit crabs, some of which spend all or nearly all of their time in the water, 

 agree with the Bracliyoura in having a corneal membrane comiiosed of hexagonal facets, not to 

 speak of other Macrourau forms which are invariably aquatic, like Al|)lieus, in which the hexagonal 

 system is retained or there is a transitional conditi<m between the hexagon and the square in the 

 eye of the adult. 



We do not yet know the physical or physiological signiticance of these two kinds of facets, 

 and possibly in this fact lies the root of the difficulty pointed out above. 



The hexagonal arrangement is the natural one. lor tubes with elastic walls <o assume when 

 there is sufficient mutual pressure, and it is also the most economical arrangement, so far as wall 

 Space is concerned, for regular prisms of equal capacity. Next to this in point of economy of wall 

 space comes the square prism, and next to this the triangular prism, where, as before, all available 

 space is occupied. This last arrangement, however, is not regularly assumed. 



If a given number of hexagonal prisms occupying a given space tend to increase in size, then 

 they would tend also to assume another form less economical of wall space, such as the square 

 prism. If the wall area of the hexagonal jirism remains the same and the number of prisms 

 increases in a given space, then each prism must be less economical of wall area and assume 

 another form like that of the square prism. 



If we nmy apply the same principles to the growing ommatidia, it is possible that crowding 

 may have something to do with the change. 



In the h)bster the change from the hexagonal to the tetragonal system is attended by a growth 

 of the ommatidium in all directions and by the addition of new ommatidia. If an outline drawing 

 of the eye of the first larva of the lobster be compareil with a similar one of the fifth larva, it will 

 be seen that the convexity of the outer surface, that is, the area of the eye, has very greatly 

 increased, whereas the diameter of the eye stalk has remained very nearly the same. During 

 this period the change from the hexagon to the square has been begun. During this time the 

 ommatidia have increased in length with the increasing convexity of the cornea, and they have also 

 increased in sectional area and in actual number. It is a very noticeable fact also that in the 

 lobster the eye stalk is compressed dorso-ventrally, so that the horizontal radius of curvature 

 of the retinal surface is considerably greater than the vertical radius of curvature. Furthermore, 

 the sides of the hexagonal facets which suffer reduction lie in a vertical plane, indicating a strain 

 or pressun^ iu a dorso-veutral direction. 



in Alphtus miulvj/i the relative increase in the convexity of the corneal cuticula is very slight 

 in passing from the first larva (length, about i""") to later stages, and the eye of an adult (i;i""" 

 long) is only about one-fourth larger than that of the larva at the time of hatching. Moreover, in 

 Alj)heus the convex surface of the eye is nearly a jjerfect hemisphere, the curvatures being the 

 same in every plane. 



If we examine the eyes of a crab in a similar way we find that the area of the surface of the 

 retina increases less rapidly in passing from the zoiia to the megalops stage than in the case of 

 the lobster in going from the first to the fourth larval forms. The comparison, however, is of little 

 value since the lobster has an abbreviated develojiment. The eye stalk of the adult crab jiresents 

 a large retinal surface, but it pioserves a nearly cylindrical (orm, although the radii of (curvature of 

 the retinal surface are very une<]ual. In the hermit crab (in a single speeie^s examined) the hexag- 

 onal arrangement is i)reserved, not, however, without indications of a ten«lency to become tetrag- 

 onal, the hexagons becoming asymmetrical in certain parts of the eye. There is, however, the 

 same compression of the eye stalk iu a dorso- ventral plane as we see in the lobster. 



It has seemed to me worth while to jioint out these facts as ottering .some suggestions to the 

 problems under discussion, although I make no attempt at a mechanical explanation. 

 S. Mis. 94 29- 



